Seminar

The Harper-Hofstadter model describes particles in two-dimensional (2D) lattices subjected to a uniform magnetic field. Ultracold atomic gases in optical lattices are an ideal platform to study this model, thanks to their capability for realizing large and tunable magnetic fluxes per lattice plaquette. We experimentally assembled such a 2D lattice rolled into a long tube, just 3-site around, thereby realizing periodic boundary conditions. These three sites were constructed from a synthetic dimension built from the atoms’ internal degrees of freedom.

In this thesis, we begin by reviewing some of the most important Hamiltonian simulation algorithms that are applied in simulation of quantum field theories. Then we focus on state preparation which has been the slowest subroutine in previously known algorithms. We present two distinct methods that improve upon prior results. The first method utilizes classical computational tools such as Density  Matrix Renormalization Group to produce an efficient quantum algorithm for simulating fermionic quantum field theories in 1+1 dimensions.

Topological band theory was developed to predict and explain robust features in the ground state electronic structure of insulators and superconductors. A topological material is characterized by gapless modes localized at the boundary of the sample, which dictate the low-energy response. What are the fate of these edge modes when the system starts to couple to an environment? In this talk, I will present a topological classification [1] applicable to open fermionic systems governed by a general class of Lindblad master equations.

Engineering and probing the topological order is an outstanding challenge in the current quantum simulators and of fundamental importance in the condensed matter physics. A great experimental efforts have been devoted to engineering strongly-correlated system and the topologically non-trivial band structure which makes the realization of the fractional quantum Hall liquid in the quantum simulators possible in the near future.

A long-standing puzzle in quantum complexity theory is to understand the power of the class MIP* of multiprover interactive proofs with shared entanglement. This question is closely related to the study of entanglement through non-local games, which dates back to the pioneering work of Bell. In this work we show that MIP* contains NEEXP (non-deterministic doubly exponential time), exponentially improving the prior lower bound of NEXP due to Ito and Vidick.

Suppose we know densities of eigenvalues/energy levels of two Hamiltonians HA and HB. Can we find the eigenvalue distribution of the joint Hamiltonian HA+HB? Free probability theory (FPT) answers this question under certain conditions. My goal is to show that this result is helpful in physical problems, especially finding the energy gap and predicting quantum phase transitions.

Quantum computing, once just a theoretical field, is quickly advancing as physical quantum technology increases in size, capability, and reliability. In order to fully harness the power of a general quantum computer or an application-specific device, compilers and tools must be developed that optimize specifications and map them to a realization on a specific architecture. In this talk, a technique and prototype tool for synthesizing algorithms into a quantum computer is described.

Topological order can be found in a wide range of physical systems, from crystalline solids, photonic meta-materials and even atmospheric waves to optomechanic, acoustic and atomic systems. Topological systems are a robust foundation for creating quantized channels for transporting electrical current, light, and atmospheric disturbances. These topological effects are quantified in terms of integer-valued invariants, such as the Chern number, applicable to the quantum Hall effect, or the Z2 invariant suitable for topological insulators.

Looking for some fresh bathroom tiles? Why don't you try regular 7-gons this time, it looks really cool! Only requirement would be that you live in hyperbolic space of constant negative curvature.

We study the connection between the charging power of a quantum battery and the fluctuations of the work stored in the battery. We show that in order to have a non-zero rate of change of the extractable work, the work fluctuations must be non-zero. This is presented in terms of an uncertainty relationship that bounds the speed of the charging process of any quantum system. Our findings also identify quantum coherence in the battery as a resource in the charging process, which we illustrate on a toy model of a heat engine.